Practical equilibrium constant

However, for most reactions in solution, a less rigorously defined practical equilibrium constant, derived from Equation 3.9 and expressed in terms of molar concentrations of species at equilibrium, may be sufficient, and we note that, defined in Equation 3.10, Kc is not dimensionless, but has units (unless [vx + Vy + ] = [va + + ]) ... 

The practical equilibrium constant has units, which depend upon the type of reaction. Consider, for example, a reaction of the type... 

We recall that the (practical) equilibrium constant (concentration ratio) is given by K=kjk . Thus we may formally express K of ionic (-dipolar) equilibria of the type (2.13) by... 

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

Figure B2.5.7 shows the absorption traces of the methyl radical absorption as a fiinction of tune. At the time resolution considered, the appearance of CFt is practically instantaneous. Subsequently, CFl disappears by recombination (equation B2.5.28). At temperatures below 1500 K, the equilibrium concentration of CFt is negligible compared witli (left-hand trace) the recombination is complete. At temperatures above 1500 K (right-hand trace) the equilibrium concentration of CFt is appreciable, and thus the teclmique allows the detennination of botli the equilibrium constant and the recombination rate [54, M]. This experiment resolved a famous controversy on the temperature dependence of the recombination rate of methyl radicals. Wliile standard RRKM theories [, ] predicted an increase of the high-pressure recombination rate coefficient /r (7) by a factor of 10-30 between 300 K and 1400 K, the statistical-adiabatic-chaunel model predicts a...

Ihe allure of methods for calculating free energies and their associated thermod)mai values such as equilibrium constants has resulted in considerable interest in free ene calculations. A number of decisions must be made about the way that the calculatior performed. One obvious choice concerns the simulation method. In principle, eit Monte Carlo or molecular dynamics can be used in practice, molecular dynamics almost always used for systems where there is a significant degree of conformatio flexibility, whereas Monte Carlo can give very good results for small molecules which either rigid or have limited conformational freedom. 

The Effect of Ionic Strength on an Equilibrium Constant (A Class Study). In J. A. Bell, ed. Chemical Principles in Practice. Addison-Wesley Reading, MA, 1967. 

The product is equal to the equilibrium constant X for the reaction shown in equation 30. It is generally considered that a salt is soluble if > 1. Thus sequestration or solubilization of moderate amounts of metal ion usually becomes practical as X. approaches or exceeds one. For smaller values of X the cost of the requited amount of chelating agent may be prohibitive. However, the dilution effect may allow economical sequestration, or solubilization of small amounts of deposits, at X values considerably less than one. In practical appHcations, calculations based on concentration equihbrium constants can be used as a guide for experimental studies that are usually necessary to determine the actual behavior of particular systems. 

Equilibrium Constants For practical application, Eq. (4-336) must be reformulated. The initial step is elimination of the in favor of fugacities. Equation (4-74) for species i in its standard state is subtracted from Eq. (4-77) for species i in the equilibrium mixture, giving... 

Since in most practical circumstances at temperatures where vapour transport is used and at around one atmosphere pressure, die atomic species play a minor role in the distribution of atoms, it is simpler to cast the distribution equations in terms of the elemental molecular species, H2, O2 and S2, tire base molecules, and the derived molecules H2O, H2S, SO2 and SO3, and eliminate any consideration of the atomic species. In this case, let X, be tire initial mole fraction of each atomic species in the original total of atoms, aird the variables Xi represent the equilibrium number of each molecular species in the final number of molecules, N/. Introducing tire equilibrium constants for the formation of each molecule from tire elemental atomic species, with a total pressure of one aurros, we can write... 

Radical substitution reactions by iodine are not practical because the abstraction of hydrogen from hydrocarbons by iodine is endothermic, even for stable radicals. The enthalpy of the overall reaction is also slightly endothermic. Thus, because of both the kinetic problem excluding a chain reaction and an unfavorable equilibrium constant for substitution, iodination cannot proceed by a radical-chain mechanism. 

Some chemical reactions are reversible and, no matter how fast a reaction takes place, it cannot proceed beyond the point of chemical equilibrium in the reaction mixture at the specified temperature and pressure. Thus, for any given conditions, the principle of chemical equilibrium expressed as the equilibrium constant, K, determines how far the reaction can proceed if adequate time is allowed for equilibrium to be attained. Alternatively, the principle of chemical kinetics determines at what rate the reaction will proceed towards attaining the maximum. If the equilibrium constant K is very large, for all practical purposes the reaction is irreversible. In the case where a reaction is irreversible, it is unnecessary to calculate the equilibrium constant and check the position of equilibrium when high conversions are needed. 

Equation (5-43) has the practical advantage over Eq. (5-40) that the partition functions in (5-40) are difficult or impossible to evaluate, whereas the presence of the equilibrium constant in (5-43) permits us to introduce the well-developed ideas of thermodynamics into the kinetic problem. We define the quantities AG, A//, and A5 as, respectively, the standard free energy of activation, enthalpy of activation, and entropy of activation from thermodynamics we now can write... 

The equivalency of sites required for the application of these equations is seldom found in practice, although many authors apply these corrections. Benson has described an alternative procedure in which the rate and equilibrium constants are... 

The production of ammonia is of historical interest because it represents the first important application of thermodynamics to an industrial process. Considering the synthesis reaction of ammonia from its elements, the calculated reaction heat (AH) and free energy change (AG) at room temperature are approximately -46 and -16.5 KJ/mol, respectively. Although the calculated equilibrium constant = 3.6 X 108 at room temperature is substantially high, no reaction occurs under these conditions, and the rate is practically zero. The ammonia synthesis reaction could be represented as follows ... 

Because XL.q is relatively large, the reaction proceeds as written and greater than 99.999 99% of the ethylene is converted into bromoethane. For practical purposes, an equilibrium constant greater than about 103 means that the amount of reactant left over will be barely detectable (less than 0.1%). 

Equilibrium constants of weak bases can be measured in the laboratory by procedures very much like those used for weak acids. In practice, though, it is simpler to take advantage of a simple mathematical relationship between Kb for a weak base and Ka for its conjugate acid. This relationship can be derived by adding together the equations for the ionization of the weak acid HB and the reaction of the weak base B- with water ... 

It can be shown from a consideration of the overall stability constants of the ions [Ni( CN)4] 2 " (1027) and [ Ag( CN)2 ] (1021) that the equilibrium constant for the above ionic reaction is 1015, i.e. the reaction proceeds practically completely to the right. An interesting exercise is the analysis of a solid silver halide, e.g. silver chloride. 

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

A note on good practice In some cases you will see an equilibrium constant denoted KP to remind you that it is expressed in terms of partial pressures. However, the subscript P is unnecessary. 

A note on good practice Whether or not a reaction is spontaneous depends on the composition, so it is better to say that K > 1 for a reaction rather than that it is spontaneous. However, for reactions with very large equilibrium constants, it is very unlikely that the mixture of reagents prepared in the laboratory will correspond to 2 > K, and it is common to refer to such reactions as spontaneous. ... 

A note on good practice As these examples have shown, it is important to specify the chemical equation to which the equilibrium constant applies. 

Up to this point, we have focused on aqueous equilibria involving proton transfer. Now we apply the same principles to the equilibrium that exists between a solid salt and its dissolved ions in a saturated solution. We can use the equilibrium constant for the dissolution of a substance to predict the solubility of a salt and to control precipitate formation. These methods are used in the laboratory to separate and analyze mixtures of salts. They also have important practical applications in municipal wastewater treatment, the extraction of minerals from seawater, the formation and loss of bones and teeth, and the global carbon cycle. 

In discussing the elFect of structure on the stabilization of alkyl cations on the basis of the carbonylation-decarbonylation equilibrium constants, it is assumed that—to a first approximation—the stabilization of the alkyloxocarbonium ions does not depend on the structure of the alkyl group. The stabilization of the positive charge in the alkyloxocarbonium ion is mainly due to the resonance RC = 0 <-> RC = 0+, and the elFect of R on this stabilization is only of minor importance. It has been shown by Brouwer (1968a) that even in the case of (tertiary) alkylcarbonium ions, which would be much more sensitive to variation of R attached to the electron-deficient centre, the stabilization is practically independent of the structure of the alkyl groups. Another argument is found in the fact that the equilibrium concentrations of isomeric alkyloxocarbonium ions differ by at most a factor of 2-3 from each other (Section III). Therefore, the value of K provides a quantitative measure of the stabilization of an alkyl cation. In the case of R = t-adamantyl this equilibrium constant is 30 times larger than when R = t-butyl or t-pentyl, which means that the non-planar t-adamantyl ion is RT In 30= 2-1 kcal... 

However, considering practical limitations, that is, the availability of optically pure enantiomers, E values are more commonly determined on racemates by evaluating the enantiomeric excess values as a function of the extent of conversion in batch reactions. For irreversible reactions, the E value can be calculated from Equation 1 (when the enantiomeric excess ofthe product is known) or from Equation 2 (when the enantiomeric excess ofthe substrate is knovm) [la]. For reversible reactions, which may be the case in enzymatic resolution carried out in organic solvents (especially at extents of conversion higher than 40%), Equations 3 or 4, in which the reaction equilibrium constant has been introduced, should be used [lb]. 

In principle, Equation (7.28) is determined by equating the rates of the forward and reverse reactions. In practice, the usual method for determining Kkinetic is to run batch reactions to completion. If different starting concentrations give the same value for Kkinetic, the functional form for Equation (7.28) is justified. Values for chemical equilibrium constants are routinely reported in the literature for specific reactions but are seldom compiled because they are hard to generalize. 

For nonideal solutions, the thermodynamic equilibrium constant, as given by Equation (7.29), is fundamental and Ei mettc should be reconciled to it even though the exponents in Equation (7.28) may be different than the stoichiometric coefficients. As a practical matter, the equilibrium composition of nonideal solutions is usually found by running reactions to completion rather than by thermodynamic calculations, but they can also be predicted using generalized correlations. 

The activation parameters are much less sensitive to temperature changes than are rate or equilibrium constants and usually can be taken as being practically invariant in a narrow temperature interval. The considerations of this paper will be essentially confined to this first approximation with constant A H and AS. (For exceptions, see Section VILA.). 

Example provides practice in manipulating equilibrium constant expressions. 

Eor the reaction to proceed at a practical rate, the temperature must be increased. This improves the kinetics of the process but, unfortunately, the equilibrium constant falls dramatically as temperature increases. Example shows that at 773 K, a realistic temperature for the Haber reaction, the equilibrium position does not favor NH3 ... 

We consider each of these in more detail in subsequent chapters, but being able to identify types of equilibria helps greatly in solving equilibrium problems. The equilibrium constants for many of these characteristic types of equilibria have been measured and tabulated. Representative Za, K, and Kgp values appear in Appendix E, and tables that are more extensive can be found in the CRC Handbook of Chemistry and Physics. Example provides practice in identifying equilibria. 

In principle, the calculation of concentrations of species of a complexation equilibrium is no different from any other calculation involving equilibrium constant expressions. In practice, we have to consider multiple equilibria whenever a complex is present. This is because each ligand associates with the complex in a separate process with its own equilibrium expression. For instance, the silver-ammonia equilibrium is composed of two steps ... 

A homogeneous irreversible reaction is characterized by a large value of the equilibrium constant so that the reverse reaction can be ignored and the reaction can be considered to proceed only in the forward direction. There is practically no major problem in the measurement of the rate of reaction which progresses only in one direction. It is, however, known... 

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